In this paper we study a class of double phase problems involving critical growth, namely−div(|∇u|p−2∇u+μ(x)|∇u|q−2∇u)=λ|u|ϑ−2u+|u|p⁎−2uin Ω,u=0on ∂Ω, where Ω⊂RN is bounded Lipschitz domain, 1<ϑ0, respectively. Based on variational topol...

this paper presents a grid connected photovoltaic system, which acts as both power generator and active power filter (apf), based on flying capacitor multicell (fcm) converter. increase in the number of output voltage levels, natural self-balancing of flying capacitors and dc link voltage and lower power rating of components are the main futures of fcm converter compared with conventional multi...

Abstract We consider a nonlinear Dirichlet problem driven by the ( p , q )-Laplacian and with reaction having combined effects of singular term parametric $$(p-1)$$ (p-1) -superlinear perturbation. prove bifurcation-type re...

We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \sigma and \tau induced by isogenies relatively prime orders. give a structure theorem for such objects, that reveals connection to the classification bundles on curves Atiyah. As an application we prove analogue conjecture Loxton van der Poorten which has been recently proved A...

We study the p-Laplace equation with Potentials − div(|∇u|p−2∇u) + λV (x)|u|p−2u = |u|q−2u, u ∈ W 1,p(RN ), x ∈ RN where 2 ≤ p, p < q < p∗. Using a concentrationcompactness principle from critical point theory, we obtain existence, multiplicity solutions, and concentration of solutions.

In this paper, we prove that a semimartingale local time is a rough path of roughness p for any p ∈ [2, 3) and establish the integral ∫∞ −∞ g(x)dLt(x) for any finite q-variation function g (2 ≤ q < 3) using Lyons’ rough path integration theory. We therefore obtain the Meyer-Tanaka’s formula for continuous function f if ∇−f exists and is of finite q-variation when 2 ≤ q < 3. The case when 1 ≤ q ...